2021/07/27 by D. Morachis Galindo, D. Morachis, Jesús A. Maytorena
Computer Science · Mathematics · Physics and Astronomy · #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum discord #Quantum entanglement #Quantum gate #Quantum many-body systems #Quantum mechanics #Qubit #Separable state #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.1103/physreva.105.012601
published as Phys. Rev. A 105, 012601 (2022)
arxiv created 2021/07/27 · openalex publication_date 2022/01/03 · arxiv updated 2022/01/05 · openalex created_date 2022/01/26 · openalex updated_date 2026/07/28
The capacity of a quantum gate to produce entangled states on a bipartite system is quantified in terms of the entangling power. This quantity is defined as the average of the linear entropy of entanglement of the states produced after applying a quantum gate over the whole set of separable states. Here we focus on symmetric two-qubit quantum gates, acting on the symmetric two-qubit space, and calculate the entangling power in terms of the appropriate local invariant. A geometric description of the local equivalence classes of gates is given in terms of the su(3) Lie algebra root vectors. These vectors define a primitive cell with hexagonal symmetry on a plane, and through the Weyl group the minimum area on the plane containing the whole set of locally equivalent quantum gates is identified. We give conditions to determine when a given quantum gate produces maximally entangled states from separable ones (perfect entanglers). We find that these gates correspond to one-fourth of the whole set of locally distinct quantum gates. The formalism developed here is applicable to general three-level systems. Via the Majorana representation, qutrit transformations can be regarded as having entangling power and hence classified as perfect and nonperfect entanglers and be grouped into local-equivalence classes of the associated symmetric two-qubit space. The results are illustrated by an anisotropic Heisenberg model, the Lipkin-Meshkov-Glick model, and two coupled quantized oscillators with cross-Kerr interaction, which we use to obtain three-level gates relevant in qutrit quantum computation.